A sealing arrangement of this kind, which includes a sealing ring, is generally known, for example, from the German Patent Application DE 103 14 533 A1. As a sealing ring, the sealing arrangement includes a grooved ring of a tough plastic, which is disposed in a radially inwardly open U-shaped installation space of the second machine element, and is conFIGUREd as a contact seal between the two machine elements under radial preloading in the installation space. On the high-pressure side, the grooved ring has a radially outer, statically loaded sealing lip and a radially inner, dynamically loaded sealing lip. On the low-pressure side, the grooved ring has a contact surface which fittingly contacts the adjacent bounding wall. In the axial direction, the grooved ring is disposed so as to be relatively movable within the installation space. It discusses providing a special grooved ring geometry to improve the durability of the grooved ring by preventing abrasive wear to the grooved ring material, for example.